Method of producing energetic plasma for neutron production



Jan. 24, 1961 P. R. BELL ET AL METHOD OF-PRODUCING ENERCETIC PLASMA FORNEUTRON PRODUCTION Filed Aug. 7, 1958 momDOm ZO Jan. 24, 1961 P. R.BELT. ETAT. 2,969,308

METHOD OF PRODUCING ENERGETIC PLASMA FOR NEUTRON PRODUCTION Filed Aug.7, 1958 2 Sheets-Sheet 2 MOLECULAR ION SOURCE BEK LOW ENERGY NEUTRALSOURCEl B \PRESSUR|ZED WATER A N K E T E, TURBOl v GENERATORP :ELECTRICv Y POWER -q E l STEAM END HEAT lEXCHANGER PLATES l INVENTORS Perso R.Bell Rober-T J. Mock/'n Jr.

BY f Fig. A/ber Simon ATTORNEY United States Patent F METHOD OFPRODUCING ENERGETIC PLASMA FOR NEUTRON PRODUCTION Persa R. Bell, AlbertSimon, and Robert J. Mackin, Jr., Oak Ridge, Tenn., assignors Vto theUnited States of America as represented by-the United States AtomicEnergy Commission Filed Aug. 7, 1958, Ser. No. 753,845

5 Claims. (Cl. 204154.2)

This invention relates to a novel device for producing energeticneutrons and for heating a plasma and method of operation thereof.

Prior work in this ield which laid the groundwork for the devicesdescribed herein consisted of the development of high-current orenergetic arc discharges such as disclosed in the applications of JohnS. Luce, Serial No. 738,242, tiled May 27, 1958, now Patent No.2,920,234, issued January 5, 1960, and Serial No. 748,771, led July 15,1958, now Patent No. 2,927,232, issued March 1, 1960; the development ofa method for trapping atomic ions in a magnetic field by dissociation ofinjected highly energetic molecular ions by an energetic arc discharge,as disclosed in the application of John S. Luce, Serial No. 728,754,filed April 15, 1958; and the development ofthe method of fburnout byionization of neutral particles in a plasma producing device asdisclosed in the application of Albert Simon, Serial No. 732,770, filedApril 28, 1958.

The apparatus set forth in the application of Albert Simon,aforementioned, is useful and capable of producing an energetic plasma,but the size of the plasma produced is limited due to the relative smallsize of the apparatus. In order to provide a device in which a largerplasma may be obtained, it is necessary to make the de` vice muchlargerthan that set forth by Simon. However, iii a very large device, itis impractical to achieve burnout of the residual neutral particles,which is a prime necessitybefore a plasma can grow and thus reach a sizewhere it produces a substantial energization of the plasma. Burnout isimpractical in a larger device because suiciently large molecular ionbeam currents are not readily obtainable.

Another problem which is inherent in the Simon method is the existenceof the arc within the plasma boundaries. This'arc may be thought of asconstituting a body which introduces impurities which'tend to cool theplasma and itfco'ntains'ions which'kare 'cooler than the plasma byseveral -ord'ers vof' inaig'nitiide'y The injection of highlyenergeti'c-io'ns 'isf'vry effective in cleaning up these impurities, butit is quite costly to feed sucient energetic fuel to a large device at arate as fast as it is being burned.

With a knowledge of the above problems related to the apparatus setforth in the Simon application, aforementioned, in the production ofsubstantial energization of the plasma, the problem of cleaning upimpurities in such an apparatus and the feeding problem in a largedevice, it is a ,primaryl object of this invention to provide acontrolled plasma and neutron producing device in which burnout can beachieved, a plasma grown, and a substantial quan tityof neutrons can'beproduced. p

It is another object of this invention to provide a controlled plasmaand neutron producing device in which the heat drain and the impuritiesinherent in the arc ignition can tbe disposed of.

2,969,308 Patented Jan. 24, 1961 device in which some electrical powercan be produced from the reactions which take place in the plasma whichis produced in the device.

These and other objects and advantages will be apparent from aconsideration of the following detailed specifications and theaccompanying drawings wherein:

Fig. 1 shows a longitudinal cross-sectional view of one embodiment of acontrolled plasma and neutron producing device.

Fig. 2 shows a cross-sectional view of another embodiment of acontrolled plasma and neutron producing device,

, and

The primary object of the invention is provision of a I method forproducing an energetic plasma and for pro- Fig. 3 shows a schematicdiagram of a method for converting heat from the reactions in the deviceof Fig. 1 into electrical power.

The objects stated above have been achieved in the present invention byproviding mirror coils which provide a temporary magnetically confinedsubvolume region, said coils at startup having, for example, aboutone-fifth their normal operating values, initiating a plasma within thisregion by, for example, injecting high-energy molecular ions in anamount in excess of the critical input current for burnout (see theSimon application, supra, Fig. 2) into the temporary region into thepath of an energetic arc such as disclosed in the aforementioned Luceapplications, where a portion of the injected molecular ions are ldissociated into atomic ions, which are trapped by the temporary mirrorswill be increased, say by a factor of.

about 5. Simultaneously, the arc is shut olf, high-energy injection isdiscontinued and injection of cold fuel at an angle greater than thecritical angle for containment and through the mirror region, forexample, is begun. Cold fuel as used herein is fuel of a temperaturebelow that for optimum reaction rates, as fully discussed below. Theaddition of suicient cold fuel causes the temperature of the plasma tofall. The injection preferably continues until the temperature falls tothat corresponding to the maximum reaction ratel for a given machine. Atthat time the cold feed is adjusted to maintain the optimum reactiontemperature. Alter the subvolume is filled with a hot plasma, thereacting volume is gradually increased by proper manipulation of currentin the magnetic coils surrounding the device and the fuel feedcontrolled until the entire working volume of the device is filled withan energetic plasma. Finally, the plasma temperature is reduced to anoperating value corresponding to the injection of fresh fuel as rapidlyas fuel is lost and burned.

A brief description of the subject matter of the aforementionedapplications will now be Agiven to provide a better understanding of theoperation of the instant invention. Y

In the application of John S. Luce, Serial No. 738,242, filed May 27,1958, now Patent No. 2,920,234, issued January 5, 1960, there isdisclosed an apparatus for producing an energetic carbon arc dischargesuitable for dissociation of molecular ions into atomic ions. In thatapplication, an energetic carbon are is produced between widely spacedcarbon electrodes disposed in an evacuated chamber and in a strongmagnetic field. At startup, gas is K fed to the face of a bored cathode,a R.F. voltage source is temporarily applied between the electrodes anda varialn the applications of John S. Luce, Serial No. 748,771;

filed July 15, 1958, now Patent No. 2,927,232, issued March 1, 1960,andPersa R. Bell andrJohn Sr. Luce, serial N0. 750,834,"1ei July 24,41.953, new. nare/rit ne. 2,920,235, issued January 5, 196`Q, `t`hereare'disclosed apparatuses for producing ank energetic deuterium arcdischarge which also suitable `for *dissociationh of niolecf` ular ionsinto atomic ions. VVAIn those applicationshan energeticV gas disch-argeisproduced` between a hollow elongated cup-shaped cathode electrodeancla hollow anode electrode disposed in an evacuated Chamberland inanstronglmagnetiefield. Deuterium gas is fed to the inside f .at least@ne Qf. .Sadhollow electrodes @inthe base thereofV at a controlled ratesuch that nearly coinplete spaceicharge neutralination occurs withinthehollow cathodeandhcaduses 4the arc dischargeAto terminate fromlwithin the hollow cathode. As in the carbon arc,rdescribed above,an.`R.F. voltage source is used to help initiate the discharge and is thendisconnected. .Avatiable. `@patatinaiwtential isalSQ connected, acrosstheA electrodes'. The deuterium arc depends upon cross` iield emissionwithinwthe hollow cathode. `This cross-held emissionin thevathode andthe cup-shaped configuration, ofthe anode causesufeed gas to becompletely ionized before it leaves the electrodes. It is this completeionization of thehfeecl` gas` that permits the discharge to be veryenergetic nand to be operated under low pressure condi,-V tio ns`. Arccurrents of VL00 amperes and above arcob-l tainable with this arcdischarge using deuterium as a feedaas. M H In the applicationofi`JohnSLuce, Serial No. 728,754,` led,Apri ltill5-i19-5i8, thereisvdisclosed ,a system for igf uiting a plasmzhofV high-energy; ions andcontaining the' plasma in a s trongfmagnetic field. .-In the devicedescribed in thatvlapplication, llighfenergy `molecular ions1 such as.B2i-,arei injected Vinto a confining magnetic field perpendicular to thelines `of magnetic force. At some point in the orbit of these ions inthe magnetic eld, a portion of them are caused to be dissociated and/orionized by an energetic `arc dischargeto form atomic ions.- Theseresu1tantatomic ions haveA one-half the momentum of the original`molecular ions,1 when said molecularions are diatomic-,Handghencehlgtave one-half the .radiuscf curvature in theeld. VIfV thecenterof ,the orbits of these atomic ions coincides with the axis ofthemagnetic field, the ionscwill circulate in aringf.-` If.the centerofthe orbits andthe: axisof the'machine do not coincidet the" atomic ,ionorbit center` will precess aboutthe magnetic axis., rIfhepions`will-,circulate until.a-charge exchange occurs with one of the neutral.gas atoms in the system or until some other4 process causes the ions tobe lost. A

`ln the application of Albert Simon, Serial No. 732,770, field April 28,1958, Athereis disclosed a method for de-V stroying neutralparticles `ina thermonuclear device such asw disclosed` in` the" Luce application,ySerial No. 728,754, aforementioned. In order for'plasma` to build up andbecomehot, the residual neutral atoms or panticles in the device have tobe destroyed and new neutral particles have to beidestroyed as fast as`they flood into the system. ATherefis a, critical: value furthe-inputcurrent of the injected. molecular ionsat which the ions burn out orionize theneutralparticlesfas fast as they are ilooding into theplasma.` Sincewburnout is an important step in thedevices,.described...herein,a detailed discussion f thisprinciplexwillbe given below. .A

In the Simon application,` the apparatus at startupwill have, largenumbers of neutral 'particles in it and these neutral particles'cwillremove hot ions from the system because of the charge exchange process.The cross sectionffor charge exchange -is a steeply decreasing'vfunctionof the atomic ion velocity above about 30 kev.

However, even at 300 kev. it has a value (for deuterons is readily lost`to the system.. `The `ionization caused by thefast ion will remove manyneutrals by.,.this means, since the ionization` cross section;A about 4`1`( )1'1 om?, is more than 20 times largeas' fl'oif` charge exchangeat' 300 ktv.A As statedn above, there.,is', a`criticalvalue for theinput atomic current at `which the ions burnout the neutrals as fast aslthey are ioodi'g-irit the plasma. Once this valuel is exc eeded,Witheniodnsi get ahead of the neutrals and the plasma buildsy up Withinthe volume of containment produced by the magnetic mirror coils, henceburning out additional neutrals* Iand` the system cleans outithen'eutrals in the plasma interior. i

To determi-ne the actual magnitude of ciiitioal current,V pressure, andother controlled condi tio1`1s,r the effect of burnout by energetic ionshas` been investigated numeri'- cally. The buildup of 4ion density intheplasma in a minier-type device such as disclosed in` the Simonapplication, andalso the sub-volume formed by the temporarymirros in theinstantsapplication, can be expressed by the' time-dependent equatidns'ianti "0:1 u a Smic sion, current. 0f @react plasma r ensitywofneutralsuin external manifold, which is P- he probability gifuscattering into the` escape cone,

,approximately equal to LlT-cos 0c K=volume occupied by the plasmalocityiofjons i,

v0 hernial Vvelooityof neutrals:4 2,..

rpoulombcross section. in the` plasma.fonscatteiingv by multiplesmall-angle collisions through degrees cxharae exchange. cross section'a, 4ionization cross section region bounded bya surfaceformingavnangle,withthe iiilul, @the critical angle-fernuntainment.This' critical angle (0) is obtained from the expression:

v ercual to the `mirror ratio; that isgthe ratio, ofhtlie in magneticiield strength inl the mirror region, (o the axis:insideftheVrnirr'cils) tor the in 1- i i Athe Iral regionbetweii the` 4ritiirror eex fil-'ai iajfanifld, fffrea tiliiitei fN" ab `hat,region external t6,`i .iinnei'fchinlieigbounded' by iniiei liner 7, bfies 3;' and biics'V 4,in the Simon kev., for example. The coulomb cross-section values may becomputed from the formula where e is the charge on the electron, and E,is the average energy of anion in the plasma.

In the iirst equation above, the rst term on the right represents theconstant source input; the second term takes into account mirror losses;and the third term represents loss by charge exchange. In the secondequation above, the first term on the right represents the streaming oflneutrals into the plasma; the second term represents the outstreamingfrom the plasma; and the third term shows the eects of neutral burnoutby ionization and charge exchange.

As discussed above, burnout occurs at the critical point at which theneutrals are being ionized at a rate equal to the rate of their entryinto the system. The average number of neutrals ionized by a fast ionbefore the ion itself is lost can be expressed as Therefore, thecritical value of input current to obtain this critical point may beexpressed approximately as:

where I is the total current of neutrals streaming into the plasma asdefined by the formula:

The input current Ic used is the value of atomic ion current produced asa result of dissociation and/ or ionization of the molecular ion beam.Since the neutral instreaming varies linearly with pressure, the valueof critical current also varies linearly with pressure.

, Burnout is not a suddenly occuring phenomenon as the current isincreased, but rather a smooth transition over a relatively narrow rangeof current. It has been shown that for currents well above the criticalvalue, the steady-state neutral density, no, can be expressed as:

This shows that the neutral density approaches zero as I+ becomes verylarge.

Referring now to Fig. 1, which illustrates one apparatus in which theprinciples of this invention may be carried out, a cathode 8 `is mountedin member 33 and an anode 9 is mounted in a breeding blanket 1. It maybe desirable to place the anode at the extreme right end of the reactor,outside the permanent mirror and thus to run the arc over the entirelength of the machine. Gas fnom ya source 34 is fed through a tube 35 tothe inside of cathode '8. An arc-initiating-assisting means such as aR.F. voltage source 36, which may be a conventional welding source, isconnected at one side to cathode 8 by leads 37 and 38, and is connectedat its other side to anode 9 by lead 39, switch 40, lead 41, and lead42. An arc operating potential, such as a variable direct current source43 is connected at one side to the cathode 8 by leads 44 and 38, and isconnected at its other side to anode 9 by lead 45, switch 46, lead 47,and lead 42. An energetic arc discharge 10, which passes through opening28 in end plate 14, opening 29 in breeding blanket 1,v and follows themagnetic field lines as set up by the magnetic mirror coils as shown,may be initiated and sustained by apparatus such as disclosed in eitherof the aforementioned Luce applications.

' The reaction chamber 26 is defined by the breeding blanket 1 which issurrounded by magnetic mirror coils 6 2 and 3 and by a plurality ofsolenoid coils 17 disposed in end-to-end relation between the mirrorcoils 2 and 3,l Iand a pair of end plates 14 and 15 which are mounted byelectrica-l insulators 31 and 32, respectively, to the outside chamberwall 21. The end plates areA thus insulated so that they may becomecharged by ions and repel further'ions back 4into the reaction volume,and so that a current may be drained therefrom to obtain electricalpower directly. The solenoid coils 17 are also used to provide thetemporary mirror regions. The reaction chamber 26 is evacuated by vacuumpumps, not shown, through tubular members 24 and 25. An outer vacuumchamber 30 which encloses the reaction vacuum chamber 26, isevacuated'by vacuum pumps not shown through tubular members 22 and 23.High energy molecular ions, for exampleD2+ of 600 kev. energy, areinjected from a source 4, through an accelerator tube 5, through tube48, yand through an opening 16 in one of the solenoid coils 17 and theblanket 1, and then into the path of the energetic arc discharge 10,where a portion of them are dissociated to form a magnetically trappedcirculating ring 7 of atomic ions in a manner set forth in theaforementioned Luce application, Serial No. 728,754. Heat from thereactions that take place in the chamber 26 and the nuclear reactionsthat take place in the breeding blanket 1 will be removed by circulatinga pressurized liquid through tubes 18 disposed in the blanket 1, throughtubes`20 disposed adjacent to the end plate 14, and through tubes 19disposed adjacent to the end plate 15. Fig. 3 shows a schematic systemforl converting this heat into electrical energy.

The accelerator tube 5, referred to above, may be energized by aconventional high voltage generator. A suitablehigh current source ofmolecular ions from source 4 may be provided by apparatus such as setforth on pake 18 of if it is desired to impart energy to the fuel, andthrough entrance conduit 49 into the plasma region. In a mirror typemachine, such as illustrated in Fig. 1, it is difficult to inject Icoldgas into the interior of a plasma at an angle less than the criticalangle for containment due to the short life of a cold atom. The meanlife of an atom in a plasma is: v

t=- nav where n is equal to the ion density, v is equal to the ionvelocity, and r is equal to the ionization cross-section. Thecross-section (a) is about 1016 cm.2 for the device in consideration,and t is then equal to about 10- sec. It therefore follows that the meandistance a room-temperature atom can penetrate into the plasma before itbecomes ionized is -a fraction of a centimeter. Since a cold ion isincapable ofrcrossing the magnetic eld, cold atoms injected rfrom theside are prevented from reaching the plasma interior. A solution to thisproblem is to inject the cold fuel particles (neutrals and/or ions)through one of the mirrors at an angle greater than the critical anglefor containment. This critical angle is obtained from the formula:

where R is equal to the mirror ratio as discussed above and in theaforementioned Simon application. Upon ionization, the injected particleis then trapped between the mirrors and will move into the plasma alongthe field lie'which it is on. Theneutral atom'trajectory may be chosen'so that this field line is an interior field line of the plasma.'A

It has been determined that a mirror ratio ofv about 3.5 to l" isrequired for insuring the production of a copious quantity of neutronswhen a 50-50 mixture of deuterium' and tritium is used as cold fuelfeed, and the magnetic field must everywhere be strong enough toy.contain most of the alpha particles' produced in AtheD-T reaction. A

D-D reaction is not possible in magnetic mirror machineswithoutextremely highmirror' field ratios, which makes such a machineuneconomical;

The problem'of tritium conservation in a DT device" requires -thatalmost exactly one' tritium atom can be produced for every neutronproduced in a` 50-50 D-T mixture. It will, in fact, be desirable tobreed extra tritium to the maximum extent possible. This wouldnecessitate surrounding the reaction tube with a blanket 1 consist-mostly of lithium. In addition to the lithium, the blanket 1' wouldconsistof water, beryllium, andiron".

The water is used to moderate the neutrons rapidly, while the berylliumproduces extra neutrons by (n, 2n) reactions. separately. The tritiumthus produced in the blanket may then be recovered by conventionalmethods.

, VIn the apparatus, illustrated in Fig. 1, the reaction tube radius is60 cm., the blanketthickness is 60l cm., theinner diameter of thecoilsis 240 cm., the outer diameter of the coils is 480 cm., andthelength of the reaction chamber is 50 meters. 17 are not shown vintheirrtrue perspective with respect tothe radius of ,the reactionchamber 26 because of space' limitation on, the drawing.

In the initial stage of operation of the. apparatus of Fig. 1 -hayingthe4 dimensions referred to above, a sub-volume o f .theentire device isisolated magnetically by suitably energizing` different sections of thecoils 17. An additional' temporary mirror is produced about one meterfrom `the mirror 2 with a mirror ratio of 3.5 to l. The temporary mirrorformed by the coils `17 is shown by the dashed, bowed-in` field linesin' Figure 1. The sub-volume formed bythe temporary mirror and thepermanent mirror is then Substantially equal to the reaction Vchamber ofthe aforementioned, Simon application., The entire eld strengthy inthisregion ,isestablishedr at aA value about 1/s of its normalgoperatingvalue; Thus, tlie field in the' midplane of: the subfvolumeisabout 6kilogauss on the axisV and is 21- kilogauss in the coils. .The nextsection of eld coils immediatelyfollowing thetemporary mirror isreversed in current direction. This is done in order to obtain some eldlines which run up into the wall region as shown by dashed lines on thedrawing.

A high-energy vacuum carbon arc or hi-gh-energy deuteriumarc is nowstruck :between the cathode 8 and the anode9 in a manner as set forth inthe aforementioned Luceapplications. Once the archas been struck,injection ofkmolecular D21' `or DT+ ions at energies of about 6O0Nkev,and a current of about one ampere or greater is begun by use of acascade accelerator as discussed ahora The initial pressure ini thereaction chamber 26 is maintained at atvalue of about l06 mm. Hg. Theinjected molecular beam 6 is passedthrough the arc dischargel wheirekaportion, for` example, 25%,. of the molecular ions are dissociatedand`are trapped by the magnetic field and forni` a `circulatii1g- `beam 7,of atomic ions.

The initial condition which must be attained is Vthat of burnout Thepressure is low enough and the trapped beam is large enough so that theneutral particles which are ooding into the active volume are ionized byionizationnand ,charge exchangeas fastras they enter. The

The iron is used to contain the lithium and water The width of theblanket 1 and of the coils.

. lowed by the formation of a hot plasma in the sub-volume.

The resultant ion density, isdetermined by the balance between trappedcurrentand mirror losses, `with theV proviso thatl/z. The term isdefined as the ratio of plasma pressure `to magnetic field pressure. Theunit used for these pressures is dynes per square centimeter. The

ratio of these two pressures may be obtained from the equation f-nkT/(B2/811), where n is the particle density,

T is the temperature'in K., k is Boltzmanns constant,`

and B is the magnetic eld strength in gauss.'Y It is hoped that forvalues oft less than 1/2 the plasma will be held in stable equilibriumby the magnetic tield. With a field of l0 kilogauss, P=0.l5and with aninput trapped current of 200 ma., the particle' density is limited by=1/z condition for energies of the order of 100 kev. or greater.

Hence, the input current may be reduced immediately after goes to3f0kilogauss. Simultaneously, the arc is shut off,`

burnout so asuto end up, with ai plasma with a l/z.

The term P, referred to above, is the probability ofV scattering intothe escape cone, as discussed above, and is approximately equal tol--cos 9c, or

For a mirror ratio of 3.531,'` which is the case for the apparatusillustrated in Fig. l`, then" P=0.15.

Immediately following the formation of the hot plasma, the .magneticfields in Vall regions (including the temporary mirror) willb'e'inc'reased by a factor of about 5.`

Thus, the end mirror andten'iporary mirror rise `to 105 kilogaus'swhile' tlie rriidplane field` of the subvolumeA high-energy injection isdiscontinued and injection of cold` fuel.` of a l5045() mixture ofdeuterium and tritium is begun from source 11 and'at an angle greaterthan the critical angle for containment as discussed above.

, The principle reason for increasing the magnetic fields perature ofthe plasma to fall.

maximum reaction rate (calculated as being about 78` kev.) for thedevice described hereinafter. At that time; the cold feed is" adjustedto maintain the temperature It should be noted that any impurities linthe plasma that are due to the arc ignition technique will vanishrapidly after cold-fuel injection of deuterium and tritium gas is begun.

If the average energy of the plasma is above a first steady operatingpoint (plasma temperature corresponding to thermally stable steady-stateoperation) and below a second steady operating point (between kev. and122 kev. for P=0.`l5), there is an intrinsic tendency for the plasma toheat itself up. On the other hand, if

the system, this has a tendency to depress the temperature olf th'eplasma. By balancing these two effects, it is possible toma'intaain'theaverage energy at a xed level and to .increa's the totalfuel in the volume steadily. The

next stepwill than be the gradual motion of the tempor'ary mirror to theright (Fig. 1) by selective adjustment of curernt t'o the solenoid coils17, by means, not shown, with a consequent filling of the entire workingvolume. This adjustment of current to the solenoid coilscompriseslincreasing thecurrent t0 a coil 17 to the right of thetemporary mirror region to a value so as to provide a new temporarymirrior region having a eld strength of 105 kilogauss while at `the sametime reducing the curent to the coil 17 which formed the initialtemporary mirror region to a value which provides a field strength of 30kilogauss. This procedure is repeated step by step until the temporarymirror eld is finally moved adjacent to the mirorr field provided bycoil 3, after which the temporary mirror field is removed by reducingthe current to the coil 17 adjacent to mirror coil 3 to its normaloperating value so as to provide a field `strength of 30 kilogauss. YThehot plasma is then confined in the entire magnetic volume providedbetween mirror coils 2 and 3 and solenoid coils 17. As discussed belowthe entire device can be lled in about 45 seconds and the temporarymirrors provided by coils 17 will need no special windings, since atemporary overload of a section of winding for an interval of thisduration should be of no consequence. The final step is the reduction ofthe plasma temperature to the rst steady operating point (calculated tobe about 60 kev.);

`1 Thevtheory of the mode of operation for the balancing effectmentioned in the preceding paragraph is developed below:

Assume that the magnetic pressure remains constant and that the plasmapressure also is kept lixed. In this case, the rate of change of thenumber of particles in the plasma is:

Here n denotes the total ion density (n=nU-l'nT), ac is the coulombcross section for 90-deg. scattering by repeated small-angle collisions,and v is the relative collision velocity. The injected particle currentof ions is denoted by I, and V is the total volume of the plasma.

f Similarly, the time rate of change of the energy of the system, isgiven by the equation:

=VnDnTUDTvtEa 1 P) 2E] VMMP- Pmm, Vn%f (s) where Ea(=3.5 mev.) is theenergy deposited in the gas bythe He4 reaction product, and Pbrems isthe bremsstrahllklngloss.` The last term on the right represents theWorkfdone against the magnetic iield by the plasma. The pressure, on theassumption that the electron and ion temperatures are equal, is 4/3n. Atconstant pressure,

as follows from Equation 5 by' multiplication by 7/3.

On comparison with Equationv 8, this showsthat Hence, neutral gas mustbe fed in at a rate specified by Equation 10, which is greater than theloss rate if f 1` The volume will increase exponentially with a .timeconstant T which is Naturally, by Eq. 10, the neutral feed willnecessarily increase exponentially as well.

For our conditions,

f0.84 sec. and

T= 6.5 sec.

The total expansion of volume required to lill the entire device is ofthe order of 103. Hence, the time required is about Tm: 6.79T=45 sec.

a plus the energy needed to heat incoming cold gas particles to thetemperature of theA system. The energy depositedper unit volume per unittime is nD=deuterium ion density nT= tritium ion density aDT=nuclearcross section v=relative velocity Ea=energy of charged alpha particle(=3.5 me'v.)

1-P=probability that the alpha particle is not emitted into the mirrorloss cone If the plasma particles are distributed according to aMaxwell-Boltzmann law, the quantities a and v should be replaced yby av.This denotes the average of av overa Boltzmann distribution. In a mirrormachine, however, there will be a peaking of the distribution toward thehigher end, owing to the preferential loss of colder ions through themirrors. For this reason, a and v will be i calculated -by assuming anisotropic one-velocity distribution of ions with an energy equal to theaverage energy of the plasma particles. In this casel v Hence we chooseI where -=iaverage energy of an ion in the plasma MD=deuteron massMT=trit`on mass ll By'sirnilarreasoning;'the effective bombading energyof the deuteron is The power lostper unit volume due to bremsstrahlungisSince at equilibrium the sum of the particle loss through the mirror andthe loss by burning in the reaction must be equal to the input current,the input current per unlt volume is:

iiirsttrinon the right vaccounts for mirror lo'ss of fuel.

Thus, a@ is the Coulomb cross section for scattering through 90 deg.,and the mirror escape probability per 90 deg. collision is denoted by P.Thesecond term accounts for fuel lost by nuclear reactions.- c

Notenthat' 'a1-mirror ratio" of 3:1` is too small to permlt operation atconstant density: For amirror ratio of 3.5,- h'oweveri operation. atconstantdensity is` possible at either =60 kev. or=l22 kev. Nowtheflower the operating temperature. of asys'tem, the' higher the:density forI fixed hi-gher'the'V specicpower in-the plasma. r[his isnormally desirable, `since it results in smaller over-all devices andlwe'r capital costs.' For this reason, we choose the operation of ourdevice to be yat =60` kev; with a mirror ratio of 3.5: l. Note also thatthe point f=0 is the true ignition temperature. The gas, at thattemperature or above, will continue to `burn (though at a decreasingrate) in the absence of cold feed.

Once the operating temperature of theV system has been decided, themaximum density may be determined by specifying a value of the magneticfield. Assume that 3:30.000 gauss. Their B2 11cTg4-nil.;Tri/5'*` (18)where' is the maximum ratio of material pressure to magnetic pressure.Assume that a maximum value of @2f/ jean be achieved. Y Now if theelectrons and ions are at the same temperature and have equal densities,

F'nnfm 19) 'Ille mean residence time in the mirror system is 1 rm (20)For P==0.l5, this yields 7:0.45 sec. (21) Finally, the specific neutronproduction rate is N :nDrnTcrDTv: l .5 X 1013cm.3sec.1

As the radius of the device is increased, the nuclear power yield perunit length increases as the square of the radius. On the other hand,the total magnet power required does not change as long as the ratio ofouter coil radius to inner coil radius is kept fixed.

We consider the device to be a long solenoid. This approximation shouldbe valid, except near the mirrors. In that region, the actual magnetpower will be somewhat larger than that calculated by this method.

The magnetic field in a solenoid is given by the relation where J is thenumber of ampere turns per unit length.` If the'insideu andoutside radiiof the coils are-denoted by ri` andr2, respectively, and s is' definedas a spaceV factor equal to the fraction ofthe gross cross section ofthecoil which is occupied by solid conductor, then J 24. g (Timms whereI is the current density in the conductor. Hence` 10B :4a-s (rg-r1) (25)The ohmic power in the coils per unit length of the sole noid'is` then`Pm=I2pV (26) where p is the resistivity ofthe conductor and V is thevolumeV of the conductor per unit length of the' solenoid.

Novi V=1rs(r22r12) (27) Hence, by Equations 25, 26 and 27, the magnetpower per unit length of the solenoid may be written as wie e i Pm-41:-(12-108 (28) The resistivity of copper at 20 C. is about 2x10ohm-cm1. In addition, as will be' seen, the power density in' the coilsvwill be quite low. Hence, thef space factor We assume' .910.8'. The'choiceof;`

canlbe fairly la'rge'. rZ/rl` is somewhat arbitrary. Large values of`this ratio yield low values of the total magnet power, but at theexpense of large capital investments in copper. We' assume that r2/r1=2will be a reasonable choice.

For a eld of 30 kilogauss, we obtain Average plasma energy 60 kev.

Mirror ratio 3.5 to 1. Fuel composition 50% D, 50% T. Ion density 1.351014 ions/cm3. Magnet field (solenoid) 30 kilogauss. 1/2 Meanresidencetime 0.45 sec. Specific neutron produc- 1 tion 1.5 1013 neutrons/cm/see.Plasma `radius t 38crn. Reaction tube radius 60 cm. Flux A,on reactiontube v wall 6.05 X 1013 neutrons/cm/sec. Magnet power 1.34 mw./ m.Blanket composition Li, H2O, Be, Fe. Blanket thickness 60 cm. Coil LD.240 cm. Coil O D. 480cm. Length 50 m. Total heat power 402 Vrn'w. Totalmagnet power 67 mw.

Total weight of copper 5.4)(103 tons.

The energetic plasma produced in the device of Fig. l will effect theproduction of a quantity of neutrons and a large amount of energy. Inaddition, energy is produced by the (n, 7) reaction in the lithiumblanket. As has already been mentioned, this energy will be taken off inthe form of heat from the blanket, tube wall, and end plates and will beput through a conventional heat cycle. Fig. 3 shows such a conventionalheat cycle in which electrical power is produced.

For example, pressurized water ows through the coils in the blanket andthose adjacent the end plates, and enters a conventional heat exchangerwhere it gives up its heat to generate steam. The steam drives aturbogenerator to produce electric power in the conventional manner.

The principles set forth above may be employed in a device which istoroidal in shape. This presupposes that current theoretical ideas formaking a successful toroidal container are correct. Such a device isillustrated in Fig. 2. The device of Fig. 2 may involve the use of theenergetic arc for substantially the full length of the re actor althoughoperation of a shorter arc in the manner of Fig. l is also feasible. Thearc is terminated after burnout followed by a magnetic field increase,and relatively low energy fuel injection is used to feed the plasmaafter burnout, in the same manner as set forth in the operation of Fig.l above. The arc electrodes are positioned in a region of widelydiverging magnetic fields (a temporary condition) so that the fieldlines intersect the walls of the reaction tube. A temporary mirrorregion is established, as shown in Fig. 2, near the diverging region toform a static mirror region. This static mirror region is shown by thedashed bowed-in field lines adjacent to where tube 65 enters into thereaction chamber. In addition, a moveable mirror region is establishedto the right of the static mirror region as shown by the dashed bowed-infield lines. A small reacting plasma is initiated, by means describedabove for Fig. l, in the sub-volume between the static mirror and themoveable mirror. When burnout conditions have been achieved and thesubvolume filled, the magnetic field is increased to the value necessaryfor the containment of reaction products, the arc is extinguished, coolfuel injection is substituted, and the moveable mirror is progressivelymoved away from the static mirror until it eventually is beside theopposite side of the diverging region. At this point, the field in thediverging region is returned to normal, and both of the mirror fieldsare removed. Alternately, the field in the diverging region may bereturned to normal when the arc is extinguished.

In Fig. 2, a cathode electrode 55 is insulatingly mounted in a space inone of the solenoid coils 71, and anode electrode 56 is insulatinglymounted in one of the solenoid coils 71. These electrodes are sopositioned that the'arc discharge 57 which is initiated between thempasses through holes 75 and 76 in the blanket 70 and reaction tube 74and then follows the magnetic field lines as shown by the dashed linesAin the figure. The reaction chamber 72 is formed by the tubular member74 shaped in the form of a toroid as shown. This tube is surrounded by abreeding blanket 70. This blanket 70 is in turn surrounded by thesolenoid coils 71. Additional coils, not shown, are provided toestablish a system of transverse magnetic fields perpendicular to theaxial confining field, to insure stability of the plasma. The directionof these transverse fields rotates with axial distance around the torus.A helical confining eld is Ia simple form of such transverse field, forexample. Heat from the reaction tube and the reactions that take placein the blanket 70 is removed by pressurized fluid which is circulatedthrough tubes 69 mounted in the blanket 70. This heat is then convertedinto electrical energy in the same manner as set forth for Fig. l above.The reaction tube is evacuated by vacuum pumps not shown, throughtubular members 67 and 68. Proper energization of the solenoid coils 71provides the diverging magnetic fields and the temporary mirror elds asshown on the drawing. vHigh energy mo-V lecular ions are injected intosubvolume 73 from a source 58, through accelerator tube 59, and throughtube 60 in the form of 4a beam 61 which beam passes through arcdischarge 57 where a portion of them are dissociated to form amagnetically trapped circulating beam of atomic ions 62. When burnouthas been achieved, injection of high energy molecular ions may bestopped and injection ofcold fuel then started. This cold fuel duringthe time that a temporary mirror region exists, may be injected as abeam 66 and at an angle greater than the critical angle for containmentfrom a source 63 through tube `64, and then through tube 65, as shown.The toroid is then filled with a plasma in a manner indicated above.

The `dimensions -for the device of Fig. 2 are substantially the same asthose for Fig. 1 above and the device of Fig. 2 operates insubstantially the same manner as that set forth for Fig. l above andtherefore a detailed description of the operation of Fig. 2 will not begiven.

If a hollow deuterium arc discharge, such as disclosed in theapplication of John S. Luce, Serial No. 748,771, now Patent No.2,927,232, issued March l, 1960, aforementioned, is used in the devicesof Fig. l and Fig. 2, then the magnetic mirror fields will cause thedischarge to spread out in the region between the mirrors and the plasmawill then be contained within the hollow arc discharge. This conditionwill prevent the instreaming of cold neutrals from the vessel Walls intothe plasma.

This invention has been described by way of illustration rather thanlimitation and it should be apparent that the invention is equallyapplicable in fields other than those specified.

What is claimed is:

l. The method of initiating and sustaining an energetic plasma for theproduction of neutrons in an evacuated reaction chamber surrounded by aplurality of electromagnetic coils in end-to-end relation comprising thesteps of selectively energizing some of said coils to establish arelatively large first value of containing magnetic field in a smallportion of said chamber to form a magnetically contained sub-volume,said sub-volume being formed by two magnetic mirror regions spaced apartaxially with a uniform magnetic field therebetween and having a mirrorratio of at least 3.5 to l; initiating an energetic arc dischargebetween two electrodes, said discharge passing through said sub-volumealong the containing magnetic field lines; injecting a selected currentof relatively highenergy molecular ions into the path of said dischargewhere a portion of said molecular ions are dissociated and/or ionized toform atomic ions which are trapped by said containing magnetic field toform an energetic plasma in which neutrons are produced within saidsub-volume, said selected current being at least Igreater than thatrequired for producing a current of atomic ions sufficient to achieveburnout of neutral particles in said sub-volume; increasing the magneticfield strength of said sub-volume to a value at least five times largerthan said first value after said plasma is formed; simultaneouslyterminating said arc discharge and the injection of said high energymolecular beam, and then injecting relatively low-energy particles at aselective feed rate into said plasma until said sub-volume is filledwith a plasma; then continuing said injection of said low-energyparticles While at the same time periodically, step-by-step increasingthe length of said magnetically contained sub-volume, each said stepcomprising decreasing the current flow through the coil forming one ofsaid magnetic mirror regions to return -said one region to said uniformfield strength, and simultaneously increasing the current ow through thenext adjacent coil to thereby establish a mirror region in alignmentwith said next adjacent coil, until said sub-volume has been expanded toencompass the entire reaction chamber and is filled with an energeticplasma and a substantial quantity of neutrons.

doeegsos `2. The method set forth in' claim '1,l wherein. the reacf ftion chamber is cylindrical.

' 3;'The'method set forth rin claim r1, wherein; the reaction chamberisa torcid. f

. 4. The method set forth in claim 1, vvherein` said reec'-` 5 rtionchamber is surrounded by a .tritium breeding blanket, f and wherein thesaidl method includes'the further steps of` circulating a pressurizeduid through tubes disposed inl f .saidblanket to thereby remove heatcaused byy reactionsy in said chamber and nuclear reactions ywithin,.said blanket,

rand converting said removed heat into' electrical energy.. l f f f f 5.Thefmethod set -forth in claim 1, whereinr said lowenergyparticlesincludefboth ions'and neutral particles injected at `an angle greaterthan the critical angle for containment.

Project-Sherwood, `Amasa S. fBishopf,'Addison Wesley f Publ.y Co.,Reading, Mass., September 1958, pages '132- l Atomics andl NuclearEnergy, February 1958, pp. 58,

Nucleoncs,-February'1958, pp. 90-93, 151-155 (204- Atom, No. 25,November `1958,`Mo`nthly Information' f Bulletin of` the United. KingdomEnergy Authority,

page 13.

1. THE METHOD OF INITIATING AND SUSTAINING AN ENERGETIC PLASMA FOR THEPRODUCTION OF NEUTRONS IN AN EVACUATED REACTION CHAMBER SURROUND BY APLURALITY OF ELECTROMAGNETIC COILS IN END-TO-END RELATION COMPRISING THESTEPS OF SELECTIVELY ENERGIZING SOME OF SAID COILS TO ESTABLISH ARELATIVELY LARGE FIRST VALUE OF CONTAINING MAGNETIC FIELD IN A SMALLPORTION OF SAID CHAMBER TO FORM A MAGNETICALLY CONTAINED SUB-VOLUME,SAID SUB-VOLUME BEING FORMED BY TWO MAGNETIC MIRROR REGIONS SPACED APARTAXIALLY WITH A UNIFORM MAGNETIC FIELD THEREBETWEEN AND HAVING A MIRRORRATIO OF AT LEAST 3.5 TO 1; INITATING AN ENERGETIC ARC DISCHARGE BETWEENTWO ELECTRODES, SAID DISCHARGE PASSING THROUGH SAID SUB-VOLUME ALONG THECONTAINING MAGNETIC FIELD LINES; INJECTING A SELECTED CURRENT OFRELATIVELY HIGHENERGY MOLECULAR IONS INTO THE PATH OF SAID DISCHARGEWHERE A PORTION OF SAID MOLECULAR IONS ARE DISSOCIATED AND/OR IONIZED TOFORM ATOMIC IONS WHICH ARE TRAPPED BY SAID CONTAINING MAGNETIC FIELD TOFORM AN ENERGETIC PLASMA IN WHICH NEUTRONS ARE PRODUCED WITHIN SAIDSUB-VOLUME, SAID SELECTED CURRENT BEING AT LEAST GREATER THAN THATREQUIRED FOR PRODUCING A CURRENT OF ATOMIC IONS SUFFICIENT TO ACHIEVEBURNOUT OF NEUTRAL PARTICLES IN SAID SUB-VOLUME INCREASING THE MAGNETICFIELD STRENGTH OF SAID SUB-VOLUME TO A VALUE AT LEAST FIVE TIMES LARGERTHAN SAID FIRST VALUE AFTER SAID PLASMA IS FORMED; SIMULTANEOUSLYTERMINATING SAID ARC DISCHARGE AND THE INJECTION OF SAID HIGH ENERGYMOLECULAR BEAM, AND THEN INJECTING RELATIVELY LOW-ENERGY PARTICLES AT ASELECTED FEED RATE INTO SAID PLASMA UNTIL SAID SUB-VOLUME IS FILLED WITHA PLASMA; THEN CONTINUING SAID INJECTION OF SAID LOW-ENERGY PARTICLESWHILE AT THE SAME TIME PERIODICALLY, STEP-BY-STEP INCREASING THE LENGTHOF SAID MAGNETICALLY CONTAINED SUB-VOLUME, EACH SAID STEP COMPRISINGDECREASING THE CURRENT FLOW THROUGH THE COIL FORMING ONE OF SAIDMAGNETIC MIRROR REGIONS TO RETURN SAID ONE REGION TO SAID UNIFORM FIELDSTRENGTH, AND SIMULTANEOU-SLY INCREASING THE CURRENT FLOW THROUGH THENEXT ADJACENT COIL TO THEREBY ESTABLISH A MIRROR REGION IN ALIGNMENTWITH SAID NEXT ADJACENT COIL, UNTIL SAID SUB-VOLUME HAS BEEN EXPANDED TOENCOMPASS THE ENTIRE REACTION CHAMBER AND EXPANDED TO ENCOMPASS THEENTIRE REACTION CHAMBER QUANTITY OF NEUTRONS.